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Simplifying -7x2 + 5x + 7 = 0 Reorder the terms: 7 + 5x + -7x2 = 0 Solving 7 + 5x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.7142857143x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.7142857143x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.7142857143x + x2 = 0 + 1 -0.7142857143x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.7142857143x + x2 = 1 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 1 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 1 + 0.1275510204 Combine like terms: 1 + 0.1275510204 = 1.1275510204 0.1275510204 + -0.7142857143x + x2 = 1.1275510204 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 1.1275510204 Calculate the square root of the right side: 1.061862053 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.061862053 and -1.061862053.Subproblem 1
x + -0.3571428572 = 1.061862053 Simplifying x + -0.3571428572 = 1.061862053 Reorder the terms: -0.3571428572 + x = 1.061862053 Solving -0.3571428572 + x = 1.061862053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.061862053 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.061862053 + 0.3571428572 x = 1.061862053 + 0.3571428572 Combine like terms: 1.061862053 + 0.3571428572 = 1.4190049102 x = 1.4190049102 Simplifying x = 1.4190049102Subproblem 2
x + -0.3571428572 = -1.061862053 Simplifying x + -0.3571428572 = -1.061862053 Reorder the terms: -0.3571428572 + x = -1.061862053 Solving -0.3571428572 + x = -1.061862053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.061862053 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.061862053 + 0.3571428572 x = -1.061862053 + 0.3571428572 Combine like terms: -1.061862053 + 0.3571428572 = -0.7047191958 x = -0.7047191958 Simplifying x = -0.7047191958Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4190049102, -0.7047191958}
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